Fluxes across double-diffusive interfaces: a one-dimensional-turbulence study

This work is a parametric study of the fluxes of heat and salt across unsheared and sheared double-diffusive interfaces using one-dimensional-turbulence (ODT) simulations. It is motivated by the need to understand how these fluxes scale with parameters related to the fluid molecular properties and background shear. Comparisons are made throughout with previous models and available measurements. In unsheared interfaces, ODT simulations show that the dimensionless heat flux Nu scales with the stability parameter R., Rayleigh number Ra and Prandtl number Pr as Nu similar to(Ra/R-rho)(0.37 +/- 0.03) when Pr varies from 3 to 100 and as Nu similar to (Ra/R-rho)(0.31) Pr-0.22 +/- 0.04 when Pr varies from 0.01 to 1. Here Ra/R-rho can be seen as the ratio of destabilizing and stabilizing effects. The simulation results also indicate that the ratio of salt and heat fluxes R-f is independent of Pr, scales with the Lewis number Le as R-f similar to Le(0.41 +/- 0.04) when R-rho is large enough and deviates from this expression for low values of R-rho, when the interface becomes heavily eroded. In sheared interfaces, the simulations show three flow regimes. When the Richardson number Ri << 1, shear-induced mixing dominates, the heat flux scales with the horizontal velocity difference across the interface and R-f = R-rho. Near Ri similar to 1 the heat and salt fluxes are seen to increase abruptly as the shear increases. The flow structure and scaling of the fluxes are similar to those of unsheared interfaces when Ri >> 1.